1. Consider a perfectly competitive market with a price of $12, where each firm has a cost function of c(q) = 50+ 2q +0.5q². a) Is the market in long-run equilibrium? Explain why or why not. b) What is the value to a firm of a cost-saving process innovation that reduces the cost function to c(q) = 10 + 0.5q²? c) Illustrate this innovation graphically using a well-labeled diagram.
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In microeconomics, long run equilibrium in perfect competition refers to a state where all firms in the market are producing at minimum average cost and where the market supply equals the market demand. In this situation, there are no incentives for firms to enter or exit the market, and prices are usually determined by the intersection of supply and demand curves
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- Consider the following short-run cost curves for a perfectly competitive firm. Picture is attched If the current market price is $6, the profit-maximizing output for this firm is ____________ If the price is $6 and the firm is producing at its profit-maximizing output, then total costs for the firm are ______________ If the market price is $1, the firm will produce ______________units of output in the short run. If the price is $3 and the firm is producing at its profit-maximizing output, then the firm would make _________ profit.A firm in a perfectly competitive market has a short-run total cost function equal to SRTC=4+20q, where q is the number of units the firm produces. The firm faces a market price of $10. Enter the optimal number of units should this firm produce to profit maximize? Hint: this could be considered a "trick question", but it's easy once you think about the way a firm should profit maximize.A perfectly competitive firm’s short-run total cost curve is C(q)= 100q-4q2+0.2q3+450. What is the firm’s short-run supply curve? Determine also the output level over which the short-run supply curve is defined. How much output will the firm supply if price, p=75?
- Q)Assume that a competitive firm has the total cost function: TC=1q^3−40q^2+740q+1600 Suppose the price of the firm's output (sold in integer units) is $650 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. A. How many units should the firm produce to maximize profit? B. What is the total profit at the optimal output level? Please specify your answer as an integer.Marginal Analysis II Question 1 Assume that a competitive firm has the total cost function: TC=1q3−40q2+870q+1500TC=1q3-40q2+870q+1500 Suppose the price of the firm's output (sold in integer units) is $700 per unit. Using calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson), how many integer units should the firm produce to maximize profit? Please specify your answer as an integer. Hint 1: The first derivative of the total cost function, which is cumulative, is the marginal cost function, which is incremental. The narrated lecture and formula summary explain how to compute the derivative. Set the marginal cost equal to the marginal revenue (price in this case) to define an equation for the optimal quantity q. Rearrange the equation to the quadratic form aq2 + bq + c = 0, where a, b, and c are constants. Use the quadratic formula to solve for q: q=−b±b2−4ac−−−−−−−√2aq=-b±b2-4ac2a For non-integer quantity, round up and down to…Consider a firm in a perfectly competitive market. The firm’s marginal cost, average cost and average variable costs are given by the figure below. Suppose that the current market price is p=10. In order to maximize its profit, the firm will produce q = ___________ units of output.
- In a certain perfectly competitive market, there are 150 firms, and the short-run total cost function of each is given by Short Term Total Cost (q) = 3q³ - 16q² + 40q + 432 (note that "q" is the quantity produced by the firm). Besides that, any firm (active or potential entrant) can produce according to the total cost function Short Term Total Cost (q) = 2q³ - 16q² + 148q (desconsidering the entrance or exit of firms). Furthermore, the inverse aggregate demand function of this market corresponds to Pd(Q) = 676 - 0.56Q (which "Q" is the total quantity demanded). Based on this information, please check True or False in the arguments below: 1-The profit that each producer makes in the short-run competitive equilibrium is greater than the profit that each producer makes in the long-run competitive equilibrium. True or False? 2-In the long-term competitive equilibrium, there are 200 active firms in this market. True or False? 3-The price p* = 105 and the quantity Q* = 750 composes the…Assume the following cost data are for a purely competitive producer: Explain: “That segment of a competitive firm’s marginal cost curve that lies above its average-variable-cost curve constitutes the short-run supply curve for the firm.” Illustrate graphically. How does this curve relate to the law of diminishing returns (Chapter 6)?A firm in a perfectly competitive market faces a market price of $80, and has a total cost function: TC(Q) = Q3 – 28Q2 + 245Q + 1000. A. If the firm charges $85, how many units will they sell? B. If this firm produces Q = 15, is their profit maximized? C. If these are short run conditions and the firm is producing Q = 15, should the firm stay open or shut down temporarily? Clearly show or explain your reasoning.
- E3 Consider a perfectly competitive firm in a short run scenario. Its total cost function is TC(q)= 4q^2 + 8. The market demand function is Q(p) = 800 - 15p, and there are 40 identical firms in the market. A. What is a firm's short-run supply function? Will it ever decide to shut down? Explain. And what is the market supply function? B. Suppose there are 40 identical firms in the market. What is the equilibrium price, p*? What is the equilibrium quantity supplied by each firm, q*? What is each firm's equilibrium profit? Will there be more entry into the market? Why? C. Repeat b, but with 80 firms this time. Label your results with superscript ** D. Repeat part b, but with 280 identical firms now. Label your results by superscript ***. Part E. Compare your results in parts b - d. Explain why the increase in the number of firms affects the results in that manner. What should happen to profit eventually as the number of firms keeps increasing? And when this happens to profit,…Assume the following total cost schedule for a perfectly competitive firm. Output TVC TFC 0 0 100 1 40 100 2 70 100 3 120 100 4 180 100 5 250 100 6 330 100 The total cost of producing 6 units of output is __________________ If the firm is producing at an output level of 2 units, the ATC is _____________ and the AVC is ______________ The profit-maximizing firm would shut down in the short run if the market price of its output dropped below ___________________ At what price would a profit-maximizing firm earn zero economic profits? _______________On a graph for a representative firm in a perfectly competitive industry, depict the three cost curves AVC, ATC, and MC (assume typical U-shaped cost curves). Now assume the market price, P, is such that it intersects the upward-sloping portion of MC above ATC. Graphically depict the short-run equilibrium q (representative firm's output) and π (representative firm's profit) under this price scenario.